It really depends on what you mean by "support". Arduino has put a lot of effort into creating a boards platform and package index framework that allows the official development software to easily support any board, so in this way you could say that 3rd party boards are supported.
But as far as expecting to be able to get assistance from Arduino's private technical support staff for problems you are having that are specific to 3rd party hardware or software, it would be unreasonable to expect such a thing.
It also depends on what you mean by "non-arduino boards". Certain boards manufactured by other companies have been given special status over time because those companies had established some sort of partnership with Arduino (e.g., the "Arduino At Heart" program). You will see these listed in the Arduino IDE's Boards Manager when you don't have any 3rd party URLs added in your preferences. So these boards were given extra support, at least as far as being able to install them in the IDE without the extra step of modifying your preferences.